Data Sufficiency

The positive integers x,y, and z are such that x is a factor of y and y is a factor of z. Is z even?

(1) xz is even
(2) y is even


Can someone please help me here...?

Thanks.

Is it D?

Yes

The foundation rule here is that if x is a factor of y and y is a factor of z then x is also a factor of z. Now, you also know that y is bigger than x and z is either bigger than xy or equals to it.

Statement one tells you that xz is even. This means that one of the numbers is even. However, you also know that x is a factor of y. So if x is 3 and y is 9, then z MUST be even, or 18, for example. Sufficient.

Statement two tells you that y is even. If y is 6 and x is any odd integer, when you multiply them together, the result is always even. Now, z can have other factors, and all of them can be odd. As long as one of the factors is even, z MUST be even. Sufficient.

Choose D.

let p and q be 2 constants

question says

p.x = y
q.y = z

q(p.x) = z
qp.x = z

let qp = some constant m

mx = z

now, evaluate the options

1) xz = even

(z/m).z = even

z.z = even * m
z.z = even

therefore z = even. SUFFICIENT

2) y = even

we know, q.y = z, q.even = even

so z = even. SUFFICIENT.

(D)